def test_join(self):
p1 = Point(1, 1, 4, 0)
p2 = Point(2, 1, 5, 0)
p3 = Point(3, 4, 6, 0)
p4 = Point(0, 2, 7, 0)
p5 = Point(1, 5, 8, 0)
# 4 points
assert join(p1, p2, p3, p4).contains(p5)
# 3 points
assert join(p1, p2, p3).contains(p3)
# two lines
l = Line(p1, p2)
m = Line(p3, p4)
assert join(l, m) == Plane(p1, p2, p3, p4)
# coplanar lines
l = Line(p1, p2)
m = Line(p1, p3)
assert join(l, m).contains(p3)
# point and line
p = join(l, p3)
assert p == join(p1, p2, p3)
# 2 points
l = p1.join(p2)
assert l.contains(Point(3, 1, 6, 0))
def test_is_collinear():
p1 = Point(1, 0)
p2 = Point(2, 0)
p3 = Point(3, 0)
l = Line(p1, p2)
assert l.contains(p3)
assert is_collinear(p1, p2, p3)
p1 = PointCollection([(1, 0), (1, 1)], homogenize=True)
p2 = PointCollection([(2, 0), (2, 1)], homogenize=True)
p3 = PointCollection([(3, 0), (3, 1)], homogenize=True)
p4 = PointCollection([(4, 0), (4, 1)], homogenize=True)
assert all(is_collinear(p1, p2, p3, p4))